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E-raamat: Numerical Methods in Turbulence Simulation

Edited by (Chair, Computational Engineering and Sciences, The University of Texas at Austin, TX, USA; Director, DOE-funded Center for Predictive Engineering and Computational Sciences (PECOS))
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Numerical Methods in Turbulence Simulation provides detailed specifications of the numerical methods needed to solve important problems in turbulence simulation. Numerical simulation of turbulent fluid flows is challenging because of the range of space and time scales that must be represented. This book provides explanations of the numerical error and stability characteristics of numerical techniques, along with treatments of the additional numerical challenges that arise in large eddy simulations. Chapters are written as tutorials by experts in the field, covering specific both contexts and applications. Three classes of turbulent flow are addressed, including incompressible, compressible and reactive, with a wide range of the best numerical practices covered.

A thorough introduction to the numerical methods is provided for those without a background in turbulence, as is everything needed for a thorough understanding of the fundamental equations. The small scales that must be resolved are generally not localized around some distinct small-scale feature, but instead are distributed throughout a volume. These characteristics put particular strain on the numerical methods used to simulate turbulent flows.

  • Includes a detailed review of the numerical approximation issues that impact the simulation of turbulence
  • Provides a range of examples of large eddy simulation techniques
  • Discusses the challenges posed by boundary conditions in turbulence simulation and provides approaches to addressing them
Contributors ix
Preface xi
1 Numerical challenges in turbulence simulation
Robert D. Moser
1.1 A brief introduction to turbulence
1(12)
1.2 Numerical discretization of convection
13(16)
1.3 Numerical discretization of diffusion
29(5)
1.4 Numerical time discretization
34(7)
Acknowledgments
41(1)
References
42(3)
2 Spectral numerical methods for turbulence simulation
Robert D. Moser
2.1 Motivation
45(1)
2.2 General characteristics of spectral methods
46(15)
2.3 Fourier spectral methods
61(13)
2.4 Orthogonal polynomials
74(6)
2.5 Spectral methods with polynomial bases
80(9)
2.6 Time discretization for spectral methods
89(2)
Acknowledgments
91(1)
References
91(4)
3 Spectral element methods for turbulence
Paul F. Fischer
Ananias G. Tomboulides
3.1 Introduction
95(3)
3.2 Advection-diffusion in a single deformed element
98(10)
3.3 The multielement case
108(3)
3.4 PN -- PN formulation for incompressible flows
111(7)
3.5 PN -- PN formulation for low-Mach-number flows
118(3)
3.6 Computing the pressure
121(5)
3.7 Practical aspects
126(4)
3.8 Example applications
130(3)
References
133(6)
4 Spline-based methods for turbulence
John A. Evans
4.1 Introduction
139(5)
4.2 A brief introduction to splines
144(9)
4.3 Spline-based methods for incompressible flows
153(16)
4.4 A selection of spline velocity/pressure pairs
169(4)
4.5 Stabilized spline-based methods
173(7)
References
180(9)
5 Finite element methods for turbulence
Kenneth E. Jansen
Jed Brown
5.1 Introduction
189(2)
5.2 Discretization foundations
191(6)
5.3 Finite element formulations
197(18)
5.4 Implementation
215(12)
5.5 Scale resolving turbulence simulations
227(3)
References
230(5)
6 Finite difference methods for turbulence simulations
Aditya Ghate
Sanjiva K. Lele
6.1 Introduction
235(2)
6.2 Grid topologies
237(8)
6.3 Grid staggering and flux evaluations
245(8)
6.4 Robustness of inviscid flux discretization
253(9)
6.5 Finite difference schemes for LES: dispersion/dissipation errors
262(7)
6.6 Discretization challenges specific to incompressible flows
269(3)
6.7 Additional considerations
272(3)
6.8 Summarizing remarks
275(1)
References
276(9)
7 Unstructured finite volume approaches for turbulence
Stefan P. Domino
7.1 Introduction
285(3)
7.2 Finite volume discretization
288(11)
7.3 High Peclet number advection and diffusion
299(6)
7.4 Transient advection and diffusion illustration
305(3)
7.5 Low-Mach solver strategies
308(1)
7.6 Low-Mach fluids operators
309(1)
7.7 Validation
310(2)
Acknowledgments
312(1)
References
312(7)
8 Boundary conditions for turbulence simulation
Tim Colonius
8.1 Introduction
319(1)
8.2 A motivating example
320(5)
8.3 General framework
325(6)
8.4 BCs for compressible Navier-Stokes
331(12)
8.5 BCs for incompressible Navier-Stokes
343(6)
8.6 Turbulence modeling in boundary conditions
349(4)
8.7 BCs in other discretization schemes
353(1)
References
354(5)
9 Numerical methods in large-eddy simulation
Pierre Sagaut
9.1 Scope of the chapter
359(1)
9.2 Large-eddy simulation: from practice to theory
360(9)
9.3 Implicit coupling between numerics and explicit subgrid models
369(16)
9.4 LES numerics: beyond order of accuracy
385(3)
9.5 Concluding remarks
388(1)
References
388(5)
10 Numerical approximations formulated as LES models
Fernando F. Grinstein
Filipe S. Pereira
William J. Rider
10.1 Coarse grained simulations
393(6)
10.2 Turbulence Reynolds number and mixing transition
399(3)
10.3 Compressible numerical hydrodynamics
402(10)
10.4 Case studies
412(17)
10.5 Summary and conclusions
429(1)
Acknowledgments
430(1)
References
430(5)
11 Numerical treatment of incompressible turbulent flow
Roel W.C.P. Verstappen
Arthur E.P. Veldman
11.1 Introduction
435(3)
11.2 Flow equations
438(1)
11.3 Energy-preserving discretization
439(3)
11.4 Incompressible flow - staggered grid
442(6)
11.5 Time integration
448(2)
11.6 Numerical simulation of incompressible turbulent flow
450(7)
11.7 Counterbalancing the production of unresolved scales
457(6)
References
463(6)
12 Numerical treatment of compressible turbulent flows
Krishnan Mahesh
12.1 Introduction
469(3)
12.2 Hou and Mahesh (2005) algorithm
472(8)
12.3 Characteristic-based filtering for shock-capturing
480(7)
12.4 Multiphase compressible flows - cavitation
487(9)
12.5 Concluding remarks
496(1)
Acknowledgments
497(1)
References
497(4)
13 Numerical treatment of turbulent reacting flows
Luc Vervisch
Pascale Domingo
John Bell
13.1 Challenges in reacting flow simulations
501(1)
13.2 Modifications to the Navier-Stokes equations for reacting flows
502(10)
13.3 Scales, characteristic numbers and mesh resolution in reacting flow simulation
512(2)
13.4 Modeling subgrid scale effects in reacting flows
514(1)
13.5 Numerical formulations for reacting flows
515(8)
13.6 Numerical methods for chemistry
523(8)
13.7 Adaptive mesh refinement for reacting flows
531(4)
References
535(6)
Index 541
Robert D. Moser is W. A. "Tex" Moncrief, Jr. Chair in Computational Engineering and Sciences at The University of Texas at Austin. Before joining the faculty of The University of Texas at Austin in 2005 he was a research scientist at the NASA-Ames Research Center and then a professor of theoretical and applied mechanics at the University of Illinois. He is a faculty member of the Thermal and Fluid Systems program, and serves as the area coordinator for that program. He is also a faculty member in the Institute for Computational Engineering and Sciences, where he is serving as Deputy Director. Prof. Moser is the Director of the DOE-funded Center for Predictive Engineering and Computational Sciences (PECOS). He is a recipient of the NASA Medal for Exceptional Scientific Achievement and is a fellow of the American Physical Society.
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